statistics of extreme fluctuations in task completion landscapes
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Statistics of Extreme Fluctuations in Task Completion Landscapes. Hasan Guclu (LANL) with G. Korniss (Rensselaer). Isaac Newton Institute, Cambridge, UK; June 26-30, 2006. Motivation and introduction. Synchronization is a fundamental problem in coupled multi-component systems.

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statistics of extreme fluctuations in task completion landscapes

Statistics of Extreme Fluctuations in Task Completion Landscapes

Hasan Guclu (LANL)

with

G. Korniss (Rensselaer)

Isaac Newton Institute, Cambridge, UK; June 26-30, 2006

motivation and introduction
Motivation and introduction
  • Synchronization is a fundamental problem in coupled multi-component systems.
  • Small-World networks help autonomous synchronization. But what about extreme fluctuations? Extreme fluctuations are to be avoided for scalability and stability.
  • We discuss to what extent SW couplings lead to suppression of the extreme fluctuations.
  • One typical example of task-completion systems is Parallel Discrete-Event Simulation (PDES).
  • Stochastic time increments in task completion system correspond to noise in the associated surface growth problem. We used both exponential (short-tailed) and power-law noise (heavy-tailed).
distribution of maxima for i i d random variables
Distribution of maxima for i.i.d. random variables

Fisher-Tippett (Gumbel)

Fréchet Distribution

models
Models

Original (1D Ring)

Small-world network

dynamics in the network and observables
Dynamics in the network and observables

Coarse-grained equation of motion

Original (KPZ/EW)

SW Network

Hastings, PRL 91, 098701 (2003); Kozma, Hastings, Korniss, PRL 92, 108701 (2003)

1d ring distribution of maxima
1D ring: distribution of maxima

Raychaudhuri, PRL, ’01

Majumdar and Comtet (2004)

summary
Summary
  • Small-World links introduces a finite effective correlation length, so the system can be divided into small quasi-independent blocks.
  • When the interaction topology in a network is changed from regular lattice into small-world or scale-free, the extreme fluctuations diverge weakly (logarithmically) with the system size when the noise in the system is short-tailed and diverge in the power-law fashion when the noise is heavy-tailed noise.
  • The extreme statistics is governed by Fisher-Tippet Type I (Gumbel) distribution when noise in the system is exponential or Gaussian and Fréchet distribution in the case of power-law noise.
  • Refs: H. Guclu, G. Korniss, PRE69, 065104 (2004); H. Guclu and G. Korniss, FNL5, L43 (2005).
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